Analysis of zz-www.sudokuoftheday.co.uk-20190103-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: .8.6.4........92.3.7..2..5.6...........2..87...1..7..9...1.23......3...84...9.... initial
Autosolve
position: 283654...5..719283179.2..5.6.798....39.2..87.8.1..7..99.81723..71.43...843..9.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G6: 5 => SOL * DIS # I5: 4,6 => CTR => I5: 1,5 * PRF # I5: 1,5 => SOL * DIS # I7: 4,6 => CTR => I7: 5 * PRF # I7: 5 => SOL * DIS # B6: 4,5 => CTR => B6: 2 * DIS # I5: 4,6 => CTR => I5: 1,5 * PRF # I5: 1,5 => SOL * PRF # I5: 1,5 => SOL * DIS # I5: 4,6 => CTR => I5: 1,5 * PRF # F4: 1 => SOL * PRF # H6: 4,6 => SOL * DIS # I7: 4 => CTR => I7: 5,6 * DIS # I7: 4,6 => CTR => I7: 5 * PRF # I7: 5 => SOL * PRF # H6: 4,6 => SOL * CNT 16 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G6: 5 => SOL * STA G6: 5 * CNT 1 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.6.4........92.3.7..2..5.6...........2..87...1..7..9...1.23......3...84...9.... | initial |
| 283654...5..719283179.2..5.6.798....39.2..87.8.1..7..99.81723..71.43...843..9.... | autosolve |
| 283654197546719283179823654657981432394265871821347569968172345715436928432598716 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B2: 4,6 C2: 4,6 D3: 3,8 F3: 3,8 H1: 1,9 I1: 1,7 G3: 4,6 I3: 4,6 C5: 4,5 E5: 4,6 F5: 1,5 D6: 3,5 E6: 4,6 B7: 5,6 F8: 5,6 D9: 5,8 H7: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,F5: 1.. / F4 = 1 => 0 pairs (*) / F5 = 1 => 0 pairs (X) F5,I5: 1.. / F5 = 1 => 18 pairs (_) / I5 = 1 => 0 pairs (*) B4,B6: 2.. / B4 = 2 => 0 pairs (X) / B6 = 2 => 18 pairs (_) C8,C9: 2.. / C8 = 2 => 21 pairs (_) / C9 = 2 => 20 pairs (_) B6,H6: 2.. / B6 = 2 => 18 pairs (_) / H6 = 2 => 0 pairs (X) C8,H8: 2.. / C8 = 2 => 21 pairs (_) / H8 = 2 => 20 pairs (_) I4,I9: 2.. / I4 = 2 => 18 pairs (_) / I9 = 2 => 0 pairs (X) D3,F3: 3.. / D3 = 3 => 19 pairs (_) / F3 = 3 => 17 pairs (_) F4,D6: 3.. / F4 = 3 => 19 pairs (_) / D6 = 3 => 17 pairs (_) H4,H6: 3.. / H4 = 3 => 17 pairs (_) / H6 = 3 => 19 pairs (_) F4,H4: 3.. / F4 = 3 => 19 pairs (_) / H4 = 3 => 17 pairs (_) D6,H6: 3.. / D6 = 3 => 17 pairs (_) / H6 = 3 => 19 pairs (_) D3,D6: 3.. / D3 = 3 => 19 pairs (_) / D6 = 3 => 17 pairs (_) F3,F4: 3.. / F3 = 3 => 17 pairs (_) / F4 = 3 => 19 pairs (_) B2,C2: 4.. / B2 = 4 => 0 pairs (*) / C2 = 4 => 0 pairs (X) G3,I3: 4.. / G3 = 4 => 17 pairs (_) / I3 = 4 => 17 pairs (_) E5,E6: 4.. / E5 = 4 => 0 pairs (X) / E6 = 4 => 17 pairs (_) H7,I7: 4.. / H7 = 4 => 17 pairs (_) / I7 = 4 => 0 pairs (X) C2,C5: 4.. / C2 = 4 => 0 pairs (X) / C5 = 4 => 0 pairs (_) B7,I7: 5.. / B7 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) D6,D9: 5.. / D6 = 5 => 19 pairs (_) / D9 = 5 => 17 pairs (_) B2,C2: 6.. / B2 = 6 => 0 pairs (X) / C2 = 6 => 0 pairs (_) G3,I3: 6.. / G3 = 6 => 17 pairs (_) / I3 = 6 => 17 pairs (_) E5,E6: 6.. / E5 = 6 => 17 pairs (_) / E6 = 6 => 0 pairs (X) F8,F9: 6.. / F8 = 6 => 21 pairs (_) / F9 = 6 => 20 pairs (_) E5,I5: 6.. / E5 = 6 => 17 pairs (_) / I5 = 6 => 0 pairs (X) B2,B7: 6.. / B2 = 6 => 0 pairs (X) / B7 = 6 => 0 pairs (_) G1,I1: 7.. / G1 = 7 => 17 pairs (_) / I1 = 7 => 17 pairs (_) G9,I9: 7.. / G9 = 7 => 17 pairs (_) / I9 = 7 => 17 pairs (_) G1,G9: 7.. / G1 = 7 => 17 pairs (_) / G9 = 7 => 17 pairs (_) I1,I9: 7.. / I1 = 7 => 17 pairs (_) / I9 = 7 => 17 pairs (_) D3,F3: 8.. / D3 = 8 => 17 pairs (_) / F3 = 8 => 19 pairs (_) D9,F9: 8.. / D9 = 8 => 19 pairs (_) / F9 = 8 => 17 pairs (_) D3,D9: 8.. / D3 = 8 => 17 pairs (_) / D9 = 8 => 19 pairs (_) F3,F9: 8.. / F3 = 8 => 19 pairs (_) / F9 = 8 => 17 pairs (_) G1,H1: 9.. / G1 = 9 => 19 pairs (_) / H1 = 9 => 18 pairs (_) G8,H8: 9.. / G8 = 9 => 18 pairs (_) / H8 = 9 => 19 pairs (_) G1,G8: 9.. / G1 = 9 => 19 pairs (_) / G8 = 9 => 18 pairs (_) H1,H8: 9.. / H1 = 9 => 18 pairs (_) / H8 = 9 => 19 pairs (_) * DURATION: 0:00:46.560382 START: 02:40:34.237459 END: 02:41:20.797841 2019-05-01 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B7,C2,C5,D3,D6,D9,E5,E6,F3,F5,F8,G3,H1,H7,I1,I3) * 283654...5..719283179.2..5.6.798....39.2..87.8.1..7..99.81723..71.43...843..9.... * PAIR H1: 1,9 BLK 3 G1: 1,9,7 # reduction candidate for 1,9 G1: 7 # 17 pairs G1: 1,9 # 17 pairs * PAIR I1: 1,7 BLK 3 G1: 1,7,9 # reduction candidate for 1,7 G1: 9 # 19 pairs G1: 1,7 # 18 pairs * PAIR I1: 1,7 COL I I9: 1,7,2,5,6 # reduction candidate for 1,7 I9: 1,7 # 19 pairs I9: 2,5,6 # 17 pairs * PAIR G3: 4,6 COL G G6: 4,6,5 # reduction candidate for 4,6 G6: 5 => SOLVED * 283654197546719283179823654657981432394265871821347569968172345715436928432598716 G6: 4,6 # 23 pairs * PAIR I3: 4,6 COL I I5: 4,6,1,5 # reduction candidate for 4,6 I5: 4,6 => CTR * 283654...564719283179.2..5.6.798....3952.187.8.1..7..99581723..71.43...843..9.... I5: 1,5 => SOLVED * 283654197546719283179823654657981432394265871821347569968172345715436928432598716 I7: 4,6,5 # reduction candidate for 4,6 I7: 4,6 => CTR * 283654...564719283179.2..5.6.798....3952.187.8.1..7..99581723..71.43...843..9.... I7: 5 => SOLVED * 283654197546719283179823654657981432394265871821347569968172345715436928432598716 * PAIR C5: 4,5 BLK 4 B4: 4,5,2 # reduction candidate for 4,5 B4: 4,5 # 18 pairs B6: 4,5,2 # reduction candidate for 4,5 B6: 4,5 => CTR * 2836541975..719283179823.5.62798..3.3952.187.8413675299.817234.71243...843.598712 B6: 2 # 18 pairs * PAIR C5: 4,5 ROW 5 I5: 4,5,1,6 # reduction candidate for 4,5 I5: 4,5 # 19 pairs I5: 1,6 # 18 pairs * PAIR E5: 4,6 ROW 5 I5: 4,6,1,5 # reduction candidate for 4,6 I5: 4,6 => CTR * 283654...564719283179.2..5.6.798....3952.187.8.1..7..99581723..71.43...843..9.... I5: 1,5 => SOLVED * 283654197546719283179823654657981432394265871821347569968172345715436928432598716 * PAIR F5: 1,5 BLK 5 F4: 1,5,3 # reduction candidate for 1,5 F4: 3 # 19 pairs F4: 1,5 # 17 pairs * PAIR F5: 1,5 ROW 5 I5: 1,5,4,6 # reduction candidate for 1,5 I5: 1,5 => SOLVED * 283654197546719283179823654657981432394265871821347569968172345715436928432598716 I5: 4,6 => CTR * 283654...564719283179.2..5.6.798....3952.187.8.1..7..99581723..71.43...843..9.... * PAIR D6: 3,5 BLK 5 F4: 3,5,1 # reduction candidate for 3,5 F4: 1 => SOLVED * 283654197546719283179823654657981432394265871821347569968172345715436928432598716 F4: 3,5 # 18 pairs * PAIR E6: 4,6 ROW 6 G6: 4,6,5 # reduction candidate for 4,6 G6: 4,6 # 23 pairs H6: 4,6,2,3 # reduction candidate for 4,6 H6: 4,6 => SOLVED * 283654197546719283179823654657981432394265871821347569968172345715436928432598716 H6: 2,3 # 20 pairs * PAIR B7: 5,6 BLK 7 C8: 5,6,2 # reduction candidate for 5,6 C8: 5,6 # 20 pairs C9: 5,6,2 # reduction candidate for 5,6 C9: 5,6 # 21 pairs * PAIR B7: 5,6 ROW 7 I7: 5,6,4 # reduction candidate for 5,6 I7: 4 => CTR * 283654...564719283179.2.4566.798....3952..87.8.1..7..995817236471.43...843..9.... I7: 5,6 # 17 pairs * PAIR F8: 5,6 BLK 8 F9: 5,6,8 # reduction candidate for 5,6 F9: 5,6 # 19 pairs F9: 8 # 17 pairs * PAIR F8: 5,6 ROW 8 C8: 5,6,2 # reduction candidate for 5,6 C8: 5,6 # 20 pairs G8: 5,6,9 # reduction candidate for 5,6 G8: 5,6 # 19 pairs * PAIR D9: 5,8 BLK 8 F9: 5,8,6 # reduction candidate for 5,8 F9: 5,8 # 21 pairs F9: 6 # 20 pairs * PAIR H7: 4,6 BLK 9 I7: 4,6,5 # reduction candidate for 4,6 I7: 4,6 => CTR * 283654...564719283179.2..5.6.798....3952.187.8.1..7..99581723..71.43...843..9.... I7: 5 => SOLVED * 283654197546719283179823654657981432394265871821347569968172345715436928432598716 * PAIR H7: 4,6 COL H H6: 4,6,2,3 # reduction candidate for 4,6 H6: 4,6 => SOLVED * 283654197546719283179823654657981432394265871821347569968172345715436928432598716 H6: 2,3 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190103-absurd-base-pr-000.dot * REASONING * PRF # G6: 5 => SOL * DIS # I5: 4,6 => CTR => I5: 1,5 * PRF # I5: 1,5 => SOL * DIS # I7: 4,6 => CTR => I7: 5 * PRF # I7: 5 => SOL * DIS # B6: 4,5 => CTR => B6: 2 * DIS # I5: 4,6 => CTR => I5: 1,5 * PRF # I5: 1,5 => SOL * PRF # I5: 1,5 => SOL * DIS # I5: 4,6 => CTR => I5: 1,5 * PRF # F4: 1 => SOL * PRF # H6: 4,6 => SOL * DIS # I7: 4 => CTR => I7: 5,6 * DIS # I7: 4,6 => CTR => I7: 5 * PRF # I7: 5 => SOL * PRF # H6: 4,6 => SOL * CNT 16 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B7,C2,C5,D3,D6,D9,E5,E6,F3,F5,F8,G3,H1,H7,I1,I3) * 283654...5..719283179.2..5.6.798....39.2..87.8.1..7..99.81723..71.43...843..9.... * PAIR H1: 1,9 BLK 3 G1: 1,9,7 # reduction candidate for 1,9 G1: 7 # 17 pairs G1: 1,9 # 17 pairs * PAIR I1: 1,7 BLK 3 G1: 1,7,9 # reduction candidate for 1,7 G1: 9 # 19 pairs G1: 1,7 # 18 pairs * PAIR I1: 1,7 COL I I9: 1,7,2,5,6 # reduction candidate for 1,7 I9: 1,7 # 19 pairs I9: 2,5,6 # 17 pairs * PAIR G3: 4,6 COL G G6: 4,6,5 # reduction candidate for 4,6 G6: 5 => SOLVED * 283654197546719283179823654657981432394265871821347569968172345715436928432598716 * DURATION: 0:00:06.005589 START: 02:41:50.150574 END: 02:41:56.156163 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190103-absurd-base-pr-001.dot * REASONING * PRF # G6: 5 => SOL * STA G6: 5 * CNT 1 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190103, absurd
Solution
position: 283654197546719283179823654657981432394265871821347569968172345715436928432598716 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* INC # G1: 1,9 => UNS * INC # G1: 7 => UNS * INC # G1: 1,7 => UNS * INC # G1: 9 => UNS * INC # I9: 1,7 => UNS * INC # I9: 2,5,6 => UNS * INC # G6: 4,6 => UNS * PRF # G6: 5 => SOL * DIS # I5: 4,6 => CTR => I5: 1,5 * PRF # I5: 1,5 => SOL * DIS # I7: 4,6 => CTR => I7: 5 * PRF # I7: 5 => SOL * INC # B4: 4,5 => UNS * DIS # B6: 4,5 => CTR => B6: 2 * INC # B6: 2 => UNS * INC # I5: 4,5 => UNS * INC # I5: 1,6 => UNS * DIS # I5: 4,6 => CTR => I5: 1,5 * PRF # I5: 1,5 => SOL * INC # F4: 1,5 => UNS * INC # F4: 3 => UNS * PRF # I5: 1,5 => SOL * DIS # I5: 4,6 => CTR => I5: 1,5 * INC # F4: 3,5 => UNS * PRF # F4: 1 => SOL * INC # G6: 4,6 => UNS * PRF # H6: 4,6 => SOL * INC # H6: 2,3 => UNS * INC # C8: 5,6 => UNS * INC # C9: 5,6 => UNS * INC # I7: 5,6 => UNS * DIS # I7: 4 => CTR => I7: 5,6 * INC # F9: 5,6 => UNS * INC # F9: 8 => UNS * INC # C8: 5,6 => UNS * INC # G8: 5,6 => UNS * INC # F9: 5,8 => UNS * INC # F9: 6 => UNS * DIS # I7: 4,6 => CTR => I7: 5 * PRF # I7: 5 => SOL * PRF # H6: 4,6 => SOL * INC # H6: 2,3 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 1,9 => UNS * INC # G1: 7 => UNS * INC # G1: 1,7 => UNS * INC # G1: 9 => UNS * INC # I9: 1,7 => UNS * INC # I9: 2,5,6 => UNS * INC # G6: 4,6 => UNS * PRF # G6: 5 => SOL * STA G6: 5 * CNT 8 HDP CHAINS / 8 HYP OPENED